I don't know that there is any Perfect Messenger unless you get a custom one designed for you. They can get expensive really fast. I have been using a Chrome Citizen Messenger, and I can tell you it would meet all your criteria, except I don't see how you could carry it without going cross-body. I suspect you are going to see this on any messenger bag, however.
I would be looking for a business type backpack if you absolutely have to have the bag where you can carry it with one arm. Back sweat I have found to be basically the same with a backpack or a messenger, smaller bag = smaller sweat (in my climate anyway). There are a ton of smaller shops that make bicycle-specific backpacks, and I promise whatever you buy, you are going to find one will work for you better shortly after you buy one. Ortlieb and Thule make some backpack with some channels for airflow, although I have never seen that on a messenger.
Some of my favorite companies are: Chrome Industries, Road Runner Bags, Thule, Ortlieb just to name a few. If you look at Etsy, you can find quite a few waxed canvas messengers or backpacks that can be handmade, but I have never been brave enough to try them.